C₂₉×#3025 #16816739

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#3025

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
socle	C₂×C₂₉	C₂×#120
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

766 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 464

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(35,41)(42,45);(30,31)(32,35)(33,36)(34,37)(38,42)(39,41)(40,43)(44,45);(30,32)(31,35)(33,38)(34,39)(36,42)(37,41)(40,44)(43,45);(30,33,34,40)(31,36,37,43)(32,38,39,44)(35,42,41,45)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#13045, C₂₉×#13046, C₂₉×#21483, …
maximal normal subgroup of	C₂₉×#13045, C₂₉×#13046, C₂₉×#21483, …
maximal quotient of	C₂₉×#18122, C₂₉×#18123, C₂₉×#18124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1757);